Q6 of 23 Page 21

A transversal EF of line AB and line CD intersects the lines at point P and Q respectively. Ray PR and ray QS are parallel and bisectors of ∠ BPQ and ∠ PQC respectively.

Prove that line AB|| line CD.


ray PR ∥ SQ and PQ is transversal (given)

To find: AB ∥ CD


∠ RPQ ≅ ∠ PQS (alternate angle) two angle formed when a line crosses two other lines, that lie on opposite side of the transversal line and on opposite relative sides of the other lines. If the two lines crossed are parallel, the alternate angles are equal.)


X = y


∠ BPQ = 2x (ray PR bisect ∠ BPQ)


∠ PQC = 2y (ray SQ bisect ∠ PQC)


When a line, shape, or angle inti two exactly equal parts is called bisector.


X = y


2x = 2y (multiply 2 on both side)


∠ BPQ = ∠ PQC


But they form a pair of alternate angle that are congruent.


∴ AB ∥ CD (hence proved)


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